LMFDB - Embedded newform 888.2.br.a.569.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [888,2,Mod(473,888)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("888.473"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(888, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 0, 6, 7])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 888 = 2^{3} \cdot 3 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	888.br (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.09071569949$
Analytic rank:	$0$
Dimension:	$152$
Relative dimension:	$38$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			569.8
Character	$\chi$	$=$	888.569
Dual form			888.2.br.a.785.8

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.42713 + 0.981484i) q^{3} +(-0.212050 + 0.791381i) q^{5} +(-0.149206 - 0.258432i) q^{7} +(1.07338 - 2.80140i) q^{9} +1.40612 q^{11} +(2.07555 + 0.556143i) q^{13} +(-0.474106 - 1.33752i) q^{15} +(4.03302 - 1.08064i) q^{17} +(-4.30531 - 1.15360i) q^{19} +(0.466582 + 0.222372i) q^{21} +(3.40295 + 3.40295i) q^{23} +(3.74881 + 2.16438i) q^{25} +(1.21769 + 5.05146i) q^{27} +(-2.74173 + 2.74173i) q^{29} +(-0.659194 - 0.659194i) q^{31} +(-2.00671 + 1.38008i) q^{33} +(0.236157 - 0.0632781i) q^{35} +(-3.30552 - 5.10622i) q^{37} +(-3.50792 + 1.24344i) q^{39} +(5.90794 + 10.2328i) q^{41} +(-4.89804 + 4.89804i) q^{43} +(1.98937 + 1.44349i) q^{45} +10.9310i q^{47} +(3.45548 - 5.98506i) q^{49} +(-4.69499 + 5.50055i) q^{51} +(6.63976 + 3.83347i) q^{53} +(-0.298167 + 1.11277i) q^{55} +(7.27646 - 2.57925i) q^{57} +(-1.53365 + 0.410939i) q^{59} +(-0.777010 + 2.89984i) q^{61} +(-0.884126 + 0.140590i) q^{63} +(-0.880242 + 1.52462i) q^{65} +(-1.51826 + 0.876567i) q^{67} +(-8.19637 - 1.51650i) q^{69} +(-2.84275 + 1.64126i) q^{71} +0.542470i q^{73} +(-7.47432 + 0.590559i) q^{75} +(-0.209801 - 0.363386i) q^{77} +(4.66772 + 1.25071i) q^{79} +(-6.69572 - 6.01393i) q^{81} +(7.59339 + 4.38405i) q^{83} +3.42080i q^{85} +(1.22183 - 6.60376i) q^{87} +(1.75938 + 6.56608i) q^{89} +(-0.165959 - 0.619369i) q^{91} +(1.58774 + 0.293765i) q^{93} +(1.82588 - 3.16252i) q^{95} +(7.62300 - 7.62300i) q^{97} +(1.50930 - 3.93910i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 152 q + 4 q^{13} - 12 q^{15} + 4 q^{19} - 44 q^{31} - 12 q^{39} + 28 q^{43} + 20 q^{45} - 80 q^{49} - 12 q^{51} - 8 q^{55} - 40 q^{57} - 28 q^{61} + 48 q^{63} + 56 q^{69} + 64 q^{75} + 20 q^{79} + 16 q^{81}+ \cdots - 20 q^{97}+O(q^{100}) $ 152 * q + 4 * q^13 - 12 * q^15 + 4 * q^19 - 44 * q^31 - 12 * q^39 + 28 * q^43 + 20 * q^45 - 80 * q^49 - 12 * q^51 - 8 * q^55 - 40 * q^57 - 28 * q^61 + 48 * q^63 + 56 * q^69 + 64 * q^75 + 20 * q^79 + 16 * q^81 + 56 * q^87 + 52 * q^91 + 40 * q^93 - 20 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/888\mathbb{Z}\right)^\times$.

$n$	$223$	$409$	$445$	$593$
$\chi(n)$	$1$	$e\left(\frac{11}{12}\right)$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−1.42713	+	0.981484i	−0.823952	+	0.566660i
$3$	−1.42713	+	0.981484i	−0.823952	+	0.566660i
$4$		0			0
$5$	−0.212050	+	0.791381i	−0.0948316	+	0.353916i	−0.996994	−	0.0774806i	$-0.975312\pi$
$5$	−0.212050	+	0.791381i	−0.0948316	+	0.353916i	0.902162	+	0.431397i	$0.141979\pi$
$6$		0			0
$7$	−0.149206	−	0.258432i	−0.0563945	−	0.0976781i	0.836450	−	0.548043i	$-0.184627\pi$
$7$	−0.149206	−	0.258432i	−0.0563945	−	0.0976781i	−0.892844	+	0.450365i	$0.851294\pi$
$8$		0			0
$9$	1.07338	−	2.80140i	0.357793	−	0.933801i
$10$		0			0
$11$	1.40612			0.423961			0.211980	−	0.977274i	$-0.432009\pi$
$11$	1.40612			0.423961			0.211980	+	0.977274i	$0.432009\pi$
$12$		0			0
$13$	2.07555	+	0.556143i	0.575655	+	0.154246i	0.534889	−	0.844922i	$-0.320353\pi$
$13$	2.07555	+	0.556143i	0.575655	+	0.154246i	0.0407662	+	0.999169i	$0.487020\pi$
$14$		0			0
$15$	−0.474106	−	1.33752i	−0.122414	−	0.345347i
$16$		0			0
$17$	4.03302	−	1.08064i	0.978150	−	0.262094i	0.265885	−	0.964005i	$-0.414336\pi$
$17$	4.03302	−	1.08064i	0.978150	−	0.262094i	0.712265	+	0.701910i	$0.247669\pi$
$18$		0			0
$19$	−4.30531	−	1.15360i	−0.987706	−	0.264655i	−0.271419	−	0.962461i	$-0.587493\pi$
$19$	−4.30531	−	1.15360i	−0.987706	−	0.264655i	−0.716287	+	0.697806i	$0.754160\pi$
$20$		0			0
$21$	0.466582	+	0.222372i	0.101817	+	0.0485255i
$22$		0			0
$23$	3.40295	+	3.40295i	0.709564	+	0.709564i	0.966443	−	0.256880i	$-0.0826944\pi$
$23$	3.40295	+	3.40295i	0.709564	+	0.709564i	−0.256880	+	0.966443i	$0.582694\pi$
$24$		0			0
$25$	3.74881	+	2.16438i	0.749762	+	0.432875i
$26$		0			0
$27$	1.21769	+	5.05146i	0.234344	+	0.972154i
$28$		0			0
$29$	−2.74173	+	2.74173i	−0.509126	+	0.509126i	−0.914258	−	0.405132i	$-0.867226\pi$
$29$	−2.74173	+	2.74173i	−0.509126	+	0.509126i	0.405132	+	0.914258i	$0.367226\pi$
$30$		0			0
$31$	−0.659194	−	0.659194i	−0.118395	−	0.118395i	0.645427	−	0.763822i	$-0.276679\pi$
$31$	−0.659194	−	0.659194i	−0.118395	−	0.118395i	−0.763822	+	0.645427i	$0.776679\pi$
$32$		0			0
$33$	−2.00671	+	1.38008i	−0.349323	+	0.240242i
$34$		0			0
$35$	0.236157	−	0.0632781i	0.0399178	−	0.0106959i
$36$		0			0
$37$	−3.30552	−	5.10622i	−0.543425	−	0.839458i
$37$	−3.30552	−	5.10622i	−0.543425	−	0.839458i
$38$		0			0
$39$	−3.50792	+	1.24344i	−0.561717	+	0.199109i
$40$		0			0
$41$	5.90794	+	10.2328i	0.922665	+	1.59810i	0.795275	+	0.606249i	$0.207327\pi$
$41$	5.90794	+	10.2328i	0.922665	+	1.59810i	0.127390	+	0.991853i	$0.459340\pi$
$42$		0			0
$43$	−4.89804	+	4.89804i	−0.746945	+	0.746945i	−0.973904	−	0.226960i	$-0.927121\pi$
$43$	−4.89804	+	4.89804i	−0.746945	+	0.746945i	0.226960	+	0.973904i	$0.427121\pi$
$44$		0			0
$45$	1.98937	+	1.44349i	0.296557	+	0.215182i
$46$		0			0
$47$			10.9310i			1.59444i	0.603687	+	0.797222i	$0.293698\pi$
$47$			10.9310i			1.59444i	−0.603687	+	0.797222i	$0.706302\pi$
$48$		0			0
$49$	3.45548	−	5.98506i	0.493639	−	0.855008i
$50$		0			0
$51$	−4.69499	+	5.50055i	−0.657430	+	0.770232i
$52$		0			0
$53$	6.63976	+	3.83347i	0.912041	+	0.526567i	0.881087	−	0.472954i	$-0.156812\pi$
$53$	6.63976	+	3.83347i	0.912041	+	0.526567i	0.0309539	+	0.999521i	$0.490145\pi$
$54$		0			0
$55$	−0.298167	+	1.11277i	−0.0402048	+	0.150047i
$56$		0			0
$57$	7.27646	−	2.57925i	0.963791	−	0.341631i
$58$		0			0
$59$	−1.53365	+	0.410939i	−0.199664	+	0.0534997i	−0.357265	−	0.934003i	$-0.616291\pi$
$59$	−1.53365	+	0.410939i	−0.199664	+	0.0534997i	0.157601	+	0.987503i	$0.449624\pi$
$60$		0			0
$61$	−0.777010	+	2.89984i	−0.0994859	+	0.371287i	−0.997661	−	0.0683507i	$-0.978226\pi$
$61$	−0.777010	+	2.89984i	−0.0994859	+	0.371287i	0.898175	+	0.439637i	$0.144893\pi$
$62$		0			0
$63$	−0.884126	+	0.140590i	−0.111389	+	0.0177127i
$64$		0			0
$65$	−0.880242	+	1.52462i	−0.109181	+	0.189106i
$66$		0			0
$67$	−1.51826	+	0.876567i	−0.185485	+	0.107090i	−0.589867	−	0.807500i	$-0.700820\pi$
$67$	−1.51826	+	0.876567i	−0.185485	+	0.107090i	0.404382	+	0.914590i	$0.367487\pi$
$68$		0			0
$69$	−8.19637	−	1.51650i	−0.986727	−	0.182565i
$70$		0			0
$71$	−2.84275	+	1.64126i	−0.337372	+	0.194782i	−0.659109	−	0.752047i	$-0.729067\pi$
$71$	−2.84275	+	1.64126i	−0.337372	+	0.194782i	0.321737	+	0.946829i	$0.395733\pi$
$72$		0			0
$73$			0.542470i			0.0634913i	0.999496	+	0.0317457i	$0.0101067\pi$
$73$			0.542470i			0.0634913i	−0.999496	+	0.0317457i	$0.989893\pi$
$74$		0			0
$75$	−7.47432	+	0.590559i	−0.863061	+	0.0681919i
$76$		0			0
$77$	−0.209801	−	0.363386i	−0.0239090	−	0.0414116i
$78$		0			0
$79$	4.66772	+	1.25071i	0.525159	+	0.140716i	0.511652	−	0.859193i	$-0.329034\pi$
$79$	4.66772	+	1.25071i	0.525159	+	0.140716i	0.0135071	+	0.999909i	$0.495700\pi$
$80$		0			0
$81$	−6.69572	−	6.01393i	−0.743969	−	0.668214i
$82$		0			0
$83$	7.59339	+	4.38405i	0.833483	+	0.481212i	0.855044	−	0.518556i	$-0.173530\pi$
$83$	7.59339	+	4.38405i	0.833483	+	0.481212i	−0.0215608	+	0.999768i	$0.506864\pi$
$84$		0			0
$85$			3.42080i			0.371038i
$86$		0			0
$87$	1.22183	−	6.60376i	0.130994	−	0.707997i
$88$		0			0
$89$	1.75938	+	6.56608i	0.186494	+	0.696004i	0.994306	+	0.106564i	$0.0339848\pi$
$89$	1.75938	+	6.56608i	0.186494	+	0.696004i	−0.807812	+	0.589440i	$0.799349\pi$
$90$		0			0
$91$	−0.165959	−	0.619369i	−0.0173973	−	0.0649275i
$92$		0			0
$93$	1.58774	+	0.293765i	0.164641	+	0.0304620i
$94$		0			0
$95$	1.82588	−	3.16252i	0.187331	−	0.324467i
$96$		0			0
$97$	7.62300	−	7.62300i	0.773998	−	0.773998i	−0.204805	−	0.978803i	$-0.565656\pi$
$97$	7.62300	−	7.62300i	0.773998	−	0.773998i	0.978803	+	0.204805i	$0.0656559\pi$
$98$		0			0
$99$	1.50930	−	3.93910i	0.151690	−	0.395895i
$100$		0			0
$101$	10.6782			1.06252			0.531261	−	0.847208i	$-0.321718\pi$
$101$	10.6782			1.06252			0.531261	+	0.847208i	$0.321718\pi$
$102$		0			0
$103$	−2.74833	−	2.74833i	−0.270801	−	0.270801i	0.558621	−	0.829423i	$-0.311330\pi$
$103$	−2.74833	−	2.74833i	−0.270801	−	0.270801i	−0.829423	+	0.558621i	$0.811330\pi$
$104$		0			0
$105$	−0.274919	+	0.322090i	−0.0268294	+	0.0314328i
$106$		0			0
$107$	5.37254	−	3.10184i	0.519383	−	0.299866i	−0.217299	−	0.976105i	$-0.569725\pi$
$107$	5.37254	−	3.10184i	0.519383	−	0.299866i	0.736682	+	0.676239i	$0.236391\pi$
$108$		0			0
$109$	3.46676	+	12.9381i	0.332055	+	1.23925i	0.907026	+	0.421074i	$0.138347\pi$
$109$	3.46676	+	12.9381i	0.332055	+	1.23925i	−0.574971	+	0.818174i	$0.694987\pi$
$110$		0			0
$111$	9.72907	+	4.04291i	0.923443	+	0.383736i
$112$		0			0
$113$	−1.51522	−	5.65487i	−0.142540	−	0.531965i	−0.999853	−	0.0171696i	$-0.994534\pi$
$113$	−1.51522	−	5.65487i	−0.142540	−	0.531965i	0.857313	−	0.514796i	$-0.172132\pi$
$114$		0			0
$115$	−3.41462	+	1.97143i	−0.318415	+	0.183837i
$116$		0			0
$117$	3.78584	−	5.21751i	0.350001	−	0.482359i
$118$		0			0
$119$	−0.881022	−	0.881022i	−0.0807631	−	0.0807631i
$120$		0			0
$121$	−9.02283			−0.820257
$122$		0			0
$123$	−18.4747	−	8.80502i	−1.66581	−	0.793922i
$124$		0			0
$125$	−5.40443	+	5.40443i	−0.483387	+	0.483387i
$126$		0			0
$127$	1.72200	−	2.98260i	0.152803	−	0.264663i	−0.779454	−	0.626460i	$-0.784503\pi$
$127$	1.72200	−	2.98260i	0.152803	−	0.264663i	0.932257	+	0.361797i	$0.117837\pi$
$128$		0			0
$129$	2.18277	−	11.7975i	0.192183	−	1.03871i
$130$		0			0
$131$	−0.105122	−	0.392319i	−0.00918451	−	0.0342771i	0.961182	−	0.275917i	$-0.0889814\pi$
$131$	−0.105122	−	0.392319i	−0.00918451	−	0.0342771i	−0.970366	+	0.241640i	$0.922315\pi$
$132$		0			0
$133$	0.344249	+	1.28475i	0.0298501	+	0.111402i
$134$		0			0
$135$	−4.25584	−	0.107507i	−0.366284	−	0.00925277i
$136$		0			0
$137$		−	13.8431i		−	1.18269i	−0.806418	−	0.591346i	$-0.798597\pi$
$137$		−	13.8431i		−	1.18269i	0.806418	−	0.591346i	$-0.201403\pi$
$138$		0			0
$139$	−4.02327	−	2.32284i	−0.341250	−	0.197021i	0.319575	−	0.947561i	$-0.396460\pi$
$139$	−4.02327	−	2.32284i	−0.341250	−	0.197021i	−0.660825	+	0.750540i	$0.729793\pi$
$140$		0			0
$141$	−10.7286	−	15.5998i	−0.903507	−	1.31374i
$142$		0			0
$143$	2.91847	+	0.782003i	0.244055	+	0.0653944i
$144$		0			0
$145$	−1.58837	−	2.75113i	−0.131907	−	0.228469i
$146$		0			0
$147$	0.942841	+	11.9329i	0.0777642	+	0.984211i
$148$		0			0
$149$		−	5.47982i		−	0.448925i	−0.974483	−	0.224462i	$-0.927937\pi$
$149$		−	5.47982i		−	0.448925i	0.974483	−	0.224462i	$-0.0720626\pi$
$150$		0			0
$151$	11.8910	−	6.86525i	0.967672	−	0.558686i	0.0691465	−	0.997607i	$-0.477972\pi$
$151$	11.8910	−	6.86525i	0.967672	−	0.558686i	0.898526	+	0.438921i	$0.144639\pi$
$152$		0			0
$153$	1.30163	−	12.4580i	0.105231	−	1.00717i
$154$		0			0
$155$	0.661456	−	0.381892i	0.0531294	−	0.0306743i
$156$		0			0
$157$	−8.21847	+	14.2348i	−0.655906	+	1.13606i	0.325760	+	0.945452i	$0.394380\pi$
$157$	−8.21847	+	14.2348i	−0.655906	+	1.13606i	−0.981666	+	0.190609i	$0.938954\pi$
$158$		0			0
$159$	−13.2383	+	1.04598i	−1.04986	+	0.0829514i
$160$		0			0
$161$	0.371691	−	1.38717i	0.0292933	−	0.109324i
$162$		0			0
$163$	9.11995	−	2.44368i	0.714329	−	0.191404i	0.116689	−	0.993168i	$-0.462772\pi$
$163$	9.11995	−	2.44368i	0.714329	−	0.191404i	0.597640	+	0.801764i	$0.296105\pi$
$164$		0			0
$165$	−0.666649	−	1.88072i	−0.0518985	−	0.146414i
$166$		0			0
$167$	5.71720	−	21.3369i	0.442410	−	1.65110i	−0.280274	−	0.959920i	$-0.590425\pi$
$167$	5.71720	−	21.3369i	0.442410	−	1.65110i	0.722684	−	0.691178i	$-0.242908\pi$
$168$		0			0
$169$	−7.25970	−	4.19139i	−0.558438	−	0.322415i
$170$		0			0
$171$	−7.85294	+	10.8227i	−0.600529	+	0.827629i
$172$		0			0
$173$	1.15167	−	1.99475i	0.0875600	−	0.151658i	−0.818919	−	0.573909i	$-0.805426\pi$
$173$	1.15167	−	1.99475i	0.0875600	−	0.151658i	0.906479	+	0.422250i	$0.138760\pi$
$174$		0			0
$175$		−	1.29175i		−	0.0976470i
$176$		0			0
$177$	1.78538	−	2.09171i	0.134197	−	0.157223i
$178$		0			0
$179$	−5.02745	+	5.02745i	−0.375769	+	0.375769i	−0.869573	−	0.493804i	$-0.835606\pi$
$179$	−5.02745	+	5.02745i	−0.375769	+	0.375769i	0.493804	+	0.869573i	$0.335606\pi$
$180$		0			0
$181$	1.16321	+	2.01475i	0.0864610	+	0.149755i	0.906013	−	0.423250i	$-0.139111\pi$
$181$	1.16321	+	2.01475i	0.0864610	+	0.149755i	−0.819552	+	0.573005i	$0.805778\pi$
$182$		0			0
$183$	−1.73726	−	4.90106i	−0.128422	−	0.362297i
$184$		0			0
$185$	4.74190	−	1.53315i	0.348632	−	0.112720i
$186$		0			0
$187$	5.67090	−	1.51951i	0.414697	−	0.111118i
$188$		0			0
$189$	1.12377	−	1.06840i	0.0817424	−	0.0777143i
$190$		0			0
$191$	0.422832	+	0.422832i	0.0305950	+	0.0305950i	0.722239	−	0.691644i	$-0.243113\pi$
$191$	0.422832	+	0.422832i	0.0305950	+	0.0305950i	−0.691644	+	0.722239i	$0.743113\pi$
$192$		0			0
$193$	4.99064	−	4.99064i	0.359234	−	0.359234i	−0.504297	−	0.863531i	$-0.668248\pi$
$193$	4.99064	−	4.99064i	0.359234	−	0.359234i	0.863531	+	0.504297i	$0.168248\pi$
$194$		0			0
$195$	−0.240178	−	3.03977i	−0.0171995	−	0.217683i
$196$		0			0
$197$	−18.9245	−	10.9261i	−1.34831	−	0.778450i	−0.360303	−	0.932835i	$-0.617327\pi$
$197$	−18.9245	−	10.9261i	−1.34831	−	0.778450i	−0.988011	+	0.154386i	$0.950660\pi$
$198$		0			0
$199$	−0.872803	−	0.872803i	−0.0618714	−	0.0618714i	0.675494	−	0.737365i	$-0.263930\pi$
$199$	−0.872803	−	0.872803i	−0.0618714	−	0.0618714i	−0.737365	+	0.675494i	$0.763930\pi$
$200$		0			0
$201$	1.30641	−	2.74112i	0.0921471	−	0.193344i
$202$		0			0
$203$	1.11763	+	0.299469i	0.0784424	+	0.0210186i
$204$		0			0
$205$	−9.35085	+	2.50555i	−0.653092	+	0.174995i
$206$		0			0
$207$	13.1857	−	5.88038i	0.916468	−	0.408715i
$208$		0			0
$209$	−6.05377	−	1.62210i	−0.418748	−	0.112203i
$210$		0			0
$211$	4.17439			0.287377			0.143688	−	0.989623i	$-0.454104\pi$
$211$	4.17439			0.287377			0.143688	+	0.989623i	$0.454104\pi$
$212$		0			0
$213$	2.44609	−	5.13240i	0.167603	−	0.351666i
$214$		0			0
$215$	−2.83759	−	4.91485i	−0.193522	−	0.335190i
$216$		0			0
$217$	−0.0720013	+	0.268712i	−0.00488776	+	0.0182414i
$218$		0			0
$219$	−0.532426	−	0.774173i	−0.0359780	−	0.0523138i
$220$		0			0
$221$	8.97174			0.603504
$222$		0			0
$223$	8.30690			0.556271			0.278136	−	0.960542i	$-0.410284\pi$
$223$	8.30690			0.556271			0.278136	+	0.960542i	$0.410284\pi$
$224$		0			0
$225$	10.0872	−	8.17873i	0.672479	−	0.545249i
$226$		0			0
$227$	5.82278	−	21.7309i	0.386472	−	1.44233i	−0.449362	−	0.893350i	$-0.648349\pi$
$227$	5.82278	−	21.7309i	0.386472	−	1.44233i	0.835834	−	0.548983i	$-0.184985\pi$
$228$		0			0
$229$	4.74287	+	8.21490i	0.313418	+	0.542856i	0.979100	−	0.203380i	$-0.0651926\pi$
$229$	4.74287	+	8.21490i	0.313418	+	0.542856i	−0.665682	+	0.746236i	$0.731859\pi$
$230$		0			0
$231$	0.656070	+	0.312681i	0.0431662	+	0.0205729i
$232$		0			0
$233$	−16.8897			−1.10648			−0.553242	−	0.833021i	$-0.686610\pi$
$233$	−16.8897			−1.10648			−0.553242	+	0.833021i	$0.686610\pi$
$234$		0			0
$235$	−8.65054	−	2.31791i	−0.564299	−	0.151204i
$236$		0			0
$237$	−7.88897	+	2.79637i	−0.512444	+	0.181644i
$238$		0			0
$239$	−10.0320	+	2.68805i	−0.648913	+	0.173876i	−0.568237	−	0.822865i	$-0.692374\pi$
$239$	−10.0320	+	2.68805i	−0.648913	+	0.173876i	−0.0806757	+	0.996740i	$0.525708\pi$
$240$		0			0
$241$	0.834899	+	0.223710i	0.0537806	+	0.0144105i	0.285609	−	0.958346i	$-0.407804\pi$
$241$	0.834899	+	0.223710i	0.0537806	+	0.0144105i	−0.231828	+	0.972757i	$0.574471\pi$
$242$		0			0
$243$	15.4582	+	2.01090i	0.991645	+	0.128999i
$244$		0			0
$245$	4.00373	+	4.00373i	0.255789	+	0.255789i
$246$		0			0
$247$	−8.29433	−	4.78874i	−0.527756	−	0.304700i
$248$		0			0
$249$	−15.1396	+	1.19620i	−0.959433	+	0.0758064i
$250$		0			0
$251$	−12.8319	+	12.8319i	−0.809941	+	0.809941i	−0.984625	−	0.174684i	$-0.944110\pi$
$251$	−12.8319	+	12.8319i	−0.809941	+	0.809941i	0.174684	+	0.984625i	$0.444110\pi$
$252$		0			0
$253$	4.78495	+	4.78495i	0.300827	+	0.300827i
$254$		0			0
$255$	−3.35746	−	4.88191i	−0.210252	−	0.305717i
$256$		0			0
$257$	19.1017	−	5.11828i	1.19153	−	0.319270i	0.392040	−	0.919948i	$-0.371770\pi$
$257$	19.1017	−	5.11828i	1.19153	−	0.319270i	0.799491	+	0.600679i	$0.205103\pi$
$258$		0			0
$259$	−0.826408	+	1.61613i	−0.0513505	+	0.100421i
$260$		0			0
$261$	4.73778	+	10.6236i	0.293261	+	0.657584i
$262$		0			0
$263$	4.10210	+	7.10505i	0.252946	+	0.438116i	0.964336	−	0.264682i	$-0.0852671\pi$
$263$	4.10210	+	7.10505i	0.252946	+	0.438116i	−0.711389	+	0.702798i	$0.751934\pi$
$264$		0			0
$265$	−4.44169	+	4.44169i	−0.272851	+	0.272851i
$266$		0			0
$267$	−8.95536	−	7.64383i	−0.548059	−	0.467795i
$268$		0			0
$269$			25.5860i			1.56001i	0.625775	+	0.780004i	$0.284783\pi$
$269$			25.5860i			1.56001i	−0.625775	+	0.780004i	$0.715217\pi$
$270$		0			0
$271$	−1.63277	+	2.82804i	−0.0991836	+	0.171791i	−0.911347	−	0.411639i	$-0.864956\pi$
$271$	−1.63277	+	2.82804i	−0.0991836	+	0.171791i	0.812163	+	0.583430i	$0.198290\pi$
$272$		0			0
$273$	0.844746	+	0.721031i	0.0511264	+	0.0436388i
$274$		0			0
$275$	5.27127	+	3.04337i	0.317869	+	0.183522i
$276$		0			0
$277$	−1.51976	+	5.67181i	−0.0913134	+	0.340786i	−0.996435	−	0.0843671i	$-0.973113\pi$
$277$	−1.51976	+	5.67181i	−0.0913134	+	0.340786i	0.905121	+	0.425153i	$0.139780\pi$
$278$		0			0
$279$	−2.55423	+	1.13910i	−0.152918	+	0.0681964i
$280$		0			0
$281$	−3.39223	+	0.908944i	−0.202363	+	0.0542231i	−0.358577	−	0.933500i	$-0.616738\pi$
$281$	−3.39223	+	0.908944i	−0.202363	+	0.0542231i	0.156214	+	0.987723i	$0.450071\pi$
$282$		0			0
$283$	6.29626	−	23.4980i	0.374274	−	1.39681i	−0.480130	−	0.877198i	$-0.659410\pi$
$283$	6.29626	−	23.4980i	0.374274	−	1.39681i	0.854403	−	0.519611i	$-0.173923\pi$
$284$		0			0
$285$	0.498199	+	6.30538i	0.0295108	+	0.373499i
$286$		0			0
$287$	1.76300	−	3.05360i	0.104066	−	0.180248i
$288$		0			0
$289$	0.374993	−	0.216503i	0.0220584	−	0.0127354i
$290$		0			0
$291$	−3.39713	+	18.3608i	−0.199143	+	1.07633i
$292$		0			0
$293$	−7.86659	+	4.54178i	−0.459571	+	0.265334i	−0.711864	−	0.702317i	$-0.752149\pi$
$293$	−7.86659	+	4.54178i	−0.459571	+	0.265334i	0.252293	+	0.967651i	$0.418815\pi$
$294$		0			0
$295$		−	1.30084i		−	0.0757376i
$296$		0			0
$297$	1.71221	+	7.10295i	0.0993526	+	0.412155i
$298$		0			0
$299$	5.17048	+	8.95553i	0.299016	+	0.517912i
$300$		0			0
$301$	1.99663	+	0.534994i	0.115084	+	0.0308366i
$302$		0			0
$303$	−15.2392	+	10.4805i	−0.875467	+	0.602089i
$304$		0			0
$305$	−2.13011	−	1.22982i	−0.121970	−	0.0704194i
$306$		0			0
$307$		−	26.7723i		−	1.52797i	−0.645232	−	0.763987i	$-0.723239\pi$
$307$		−	26.7723i		−	1.52797i	0.645232	−	0.763987i	$-0.276761\pi$
$308$		0			0
$309$	6.61967	+	1.22477i	0.376580	+	0.0696749i
$310$		0			0
$311$	7.60714	+	28.3902i	0.431361	+	1.60986i	0.749627	+	0.661861i	$0.230233\pi$
$311$	7.60714	+	28.3902i	0.431361	+	1.60986i	−0.318265	+	0.948002i	$0.603100\pi$
$312$		0			0
$313$	−1.97533	−	7.37201i	−0.111652	−	0.416691i	0.887363	−	0.461072i	$-0.152535\pi$
$313$	−1.97533	−	7.37201i	−0.111652	−	0.416691i	−0.999015	+	0.0443812i	$0.985868\pi$
$314$		0			0
$315$	0.0762184	−	0.729492i	0.00429442	−	0.0411022i
$316$		0			0
$317$	15.8478	−	27.4492i	0.890103	−	1.54170i	0.0503515	−	0.998732i	$-0.483966\pi$
$317$	15.8478	−	27.4492i	0.890103	−	1.54170i	0.839751	−	0.542971i	$-0.182701\pi$
$318$		0			0
$319$	−3.85520	+	3.85520i	−0.215850	+	0.215850i
$320$		0			0
$321$	−4.62289	+	9.69978i	−0.258025	+	0.541389i
$322$		0			0
$323$	−18.6100			−1.03549
$324$		0			0
$325$	6.57715	+	6.57715i	0.364835	+	0.364835i
$326$		0			0
$327$	−17.6461	−	15.0618i	−0.975829	−	0.832917i
$328$		0			0
$329$	2.82491	−	1.63096i	0.155742	−	0.0899178i
$330$		0			0
$331$	−2.66274	−	9.93749i	−0.146358	−	0.546214i	−0.999691	−	0.0248487i	$-0.992090\pi$
$331$	−2.66274	−	9.93749i	−0.146358	−	0.546214i	0.853334	−	0.521365i	$-0.174577\pi$
$332$		0			0
$333$	−17.8527	+	3.77919i	−0.978320	+	0.207098i
$334$		0			0
$335$	−0.371752	−	1.38740i	−0.0203110	−	0.0758016i
$336$		0			0
$337$	12.1148	−	6.99446i	0.659933	−	0.381013i	−0.132318	−	0.991207i	$-0.542242\pi$
$337$	12.1148	−	6.99446i	0.659933	−	0.381013i	0.792251	+	0.610195i	$0.208909\pi$
$338$		0			0
$339$	7.71257	+	6.58305i	0.418889	+	0.357542i
$340$		0			0
$341$	−0.926905	−	0.926905i	−0.0501947	−	0.0501947i
$342$		0			0
$343$	−4.15119			−0.224143
$344$		0			0
$345$	2.93817	−	6.16488i	0.158186	−	0.331906i
$346$		0			0
$347$	11.0258	−	11.0258i	0.591895	−	0.591895i	−0.346248	−	0.938143i	$-0.612544\pi$
$347$	11.0258	−	11.0258i	0.591895	−	0.591895i	0.938143	+	0.346248i	$0.112544\pi$
$348$		0			0
$349$	−17.1968	+	29.7857i	−0.920522	+	1.59439i	−0.121913	+	0.992541i	$0.538903\pi$
$349$	−17.1968	+	29.7857i	−0.920522	+	1.59439i	−0.798609	+	0.601850i	$0.794431\pi$
$350$		0			0
$351$	−0.281960	+	11.1618i	−0.0150499	+	0.595772i
$352$		0			0
$353$	4.29977	+	16.0470i	0.228854	+	0.854093i	0.980824	+	0.194896i	$0.0624370\pi$
$353$	4.29977	+	16.0470i	0.228854	+	0.854093i	−0.751970	+	0.659197i	$0.770896\pi$
$354$		0			0
$355$	−0.696059	−	2.59773i	−0.0369430	−	0.137873i
$356$		0			0
$357$	2.12204	+	0.392620i	0.112310	+	0.0207797i
$358$		0			0
$359$			11.4435i			0.603967i	0.953313	+	0.301983i	$0.0976487\pi$
$359$			11.4435i			0.603967i	−0.953313	+	0.301983i	$0.902351\pi$
$360$		0			0
$361$	0.750403	+	0.433245i	0.0394949	+	0.0228024i
$362$		0			0
$363$	12.8767	−	8.85577i	0.675852	−	0.464807i
$364$		0			0
$365$	−0.429300	−	0.115031i	−0.0224706	−	0.00602098i
$366$		0			0
$367$	15.7524	+	27.2839i	0.822267	+	1.42421i	0.903990	+	0.427554i	$0.140625\pi$
$367$	15.7524	+	27.2839i	0.822267	+	1.42421i	−0.0817226	+	0.996655i	$0.526042\pi$
$368$		0			0
$369$	35.0078	−	5.56680i	1.82243	−	0.289796i
$370$		0			0
$371$		−	2.28790i		−	0.118782i
$372$		0			0
$373$	−24.4872	+	14.1377i	−1.26790	+	0.732021i	−0.974590	−	0.223997i	$-0.928089\pi$
$373$	−24.4872	+	14.1377i	−1.26790	+	0.732021i	−0.293308	+	0.956018i	$0.594756\pi$
$374$		0			0
$375$	2.40844	−	13.0172i	0.124371	−	0.672204i
$376$		0			0
$377$	−7.21540	+	4.16581i	−0.371612	+	0.214550i
$378$		0			0
$379$	16.7954	−	29.0905i	0.862721	−	1.49428i	−0.00657182	−	0.999978i	$-0.502092\pi$
$379$	16.7954	−	29.0905i	0.862721	−	1.49428i	0.869293	−	0.494298i	$-0.164575\pi$
$380$		0			0
$381$	0.469856	+	5.94667i	0.0240714	+	0.304657i
$382$		0			0
$383$	5.84657	−	21.8197i	0.298746	−	1.11493i	−0.639451	−	0.768832i	$-0.720838\pi$
$383$	5.84657	−	21.8197i	0.298746	−	1.11493i	0.938197	−	0.346103i	$-0.112495\pi$
$384$		0			0
$385$	0.332065	−	0.0889765i	0.0169236	−	0.00453466i
$386$		0			0
$387$	8.46394	+	18.9788i	0.430246	+	0.964749i
$388$		0			0
$389$	2.21911	−	8.28182i	0.112513	−	0.419905i	−0.886576	−	0.462584i	$-0.846923\pi$
$389$	2.21911	−	8.28182i	0.112513	−	0.419905i	0.999089	+	0.0426787i	$0.0135892\pi$
$390$		0			0
$391$	17.4015	+	10.0468i	0.880032	+	0.508087i
$392$		0			0
$393$	0.535076	+	0.456713i	0.0269910	+	0.0230381i
$394$		0			0
$395$	−1.97958	+	3.42873i	−0.0996033	+	0.172518i
$396$		0			0
$397$			21.3332i			1.07068i	0.844636	+	0.535342i	$0.179817\pi$
$397$			21.3332i			1.07068i	−0.844636	+	0.535342i	$0.820183\pi$
$398$		0			0
$399$	−1.75225	−	1.49563i	−0.0877223	−	0.0748752i
$400$		0			0
$401$	−27.1195	+	27.1195i	−1.35428	+	1.35428i	−0.473480	+	0.880804i	$0.657003\pi$
$401$	−27.1195	+	27.1195i	−1.35428	+	1.35428i	−0.880804	+	0.473480i	$0.842997\pi$
$402$		0			0
$403$	−1.00159	−	1.73480i	−0.0498926	−	0.0864166i
$404$		0			0
$405$	6.17913	−	4.02361i	0.307044	−	0.199935i
$406$		0			0
$407$	−4.64796	−	7.17995i	−0.230391	−	0.355897i
$408$		0			0
$409$	9.39205	−	2.51659i	0.464407	−	0.124437i	−0.0190257	−	0.999819i	$-0.506056\pi$
$409$	9.39205	−	2.51659i	0.464407	−	0.124437i	0.483433	+	0.875382i	$0.339390\pi$
$410$		0			0
$411$	13.5867	+	19.7558i	0.670184	+	0.974481i
$412$		0			0
$413$	0.335028	+	0.335028i	0.0164857	+	0.0164857i
$414$		0			0
$415$	−5.07963	+	5.07963i	−0.249349	+	0.249349i
$416$		0			0
$417$	8.02155	−	0.633796i	0.392817	−	0.0310371i
$418$		0			0
$419$	−12.0661	−	6.96639i	−0.589469	−	0.340330i	0.175418	−	0.984494i	$-0.443872\pi$
$419$	−12.0661	−	6.96639i	−0.589469	−	0.340330i	−0.764888	+	0.644164i	$0.777206\pi$
$420$		0			0
$421$	−24.6291	−	24.6291i	−1.20035	−	1.20035i	−0.974060	−	0.226291i	$-0.927340\pi$
$421$	−24.6291	−	24.6291i	−1.20035	−	1.20035i	−0.226291	−	0.974060i	$-0.572660\pi$
$422$		0			0
$423$	30.6220	+	11.7330i	1.48889	+	0.570480i
$424$		0			0
$425$	17.4579	+	4.67784i	0.846834	+	0.226908i
$426$		0			0
$427$	0.865346	−	0.231869i	0.0418770	−	0.0112209i
$428$		0			0
$429$	−4.93255	+	1.74842i	−0.238146	+	0.0844145i
$430$		0			0
$431$	−28.8429	−	7.72842i	−1.38931	−	0.372265i	−0.514817	−	0.857300i	$-0.672140\pi$
$431$	−28.8429	−	7.72842i	−1.38931	−	0.372265i	−0.874495	+	0.485035i	$0.838807\pi$
$432$		0			0
$433$	−15.7590			−0.757329			−0.378665	−	0.925534i	$-0.623617\pi$
$433$	−15.7590			−0.757329			−0.378665	+	0.925534i	$0.623617\pi$
$434$		0			0
$435$	4.96700	+	2.36726i	0.238149	+	0.113501i
$436$		0			0
$437$	−10.7251	−	18.5764i	−0.513050	−	0.888630i
$438$		0			0
$439$	−0.284234	+	1.06078i	−0.0135658	+	0.0506281i	−0.972377	−	0.233416i	$-0.925010\pi$
$439$	−0.284234	+	1.06078i	−0.0135658	+	0.0506281i	0.958811	+	0.284044i	$0.0916762\pi$
$440$		0			0
$441$	−13.0575	−	16.1044i	−0.621787	−	0.766877i
$442$		0			0
$443$	27.6138			1.31197			0.655985	−	0.754774i	$-0.272253\pi$
$443$	27.6138			1.31197			0.655985	+	0.754774i	$0.272253\pi$
$444$		0			0
$445$	−5.56935			−0.264012
$446$		0			0
$447$	5.37836	+	7.82040i	0.254388	+	0.369892i
$448$		0			0
$449$	7.02491	−	26.2173i	0.331526	−	1.23727i	−0.576061	−	0.817407i	$-0.695411\pi$
$449$	7.02491	−	26.2173i	0.331526	−	1.23727i	0.907587	−	0.419865i	$-0.137922\pi$
$450$		0			0
$451$	8.30726	+	14.3886i	0.391173	+	0.677532i
$452$		0			0
$453$	−10.2318	+	21.4684i	−0.480730	+	1.00867i
$454$		0			0
$455$	0.525348			0.0246287
$456$		0			0
$457$	13.4969	+	3.61649i	0.631359	+	0.169172i	0.560286	−	0.828299i	$-0.310691\pi$
$457$	13.4969	+	3.61649i	0.631359	+	0.169172i	0.0710728	+	0.997471i	$0.477358\pi$
$458$		0			0
$459$	10.3698	+	19.0567i	0.484020	+	0.889492i
$460$		0			0
$461$	−7.45297	+	1.99702i	−0.347120	+	0.0930104i	−0.428166	−	0.903700i	$-0.640840\pi$
$461$	−7.45297	+	1.99702i	−0.347120	+	0.0930104i	0.0810469	+	0.996710i	$0.474174\pi$
$462$		0			0
$463$	3.20406	+	0.858525i	0.148905	+	0.0398990i	0.332502	−	0.943103i	$-0.392107\pi$
$463$	3.20406	+	0.858525i	0.148905	+	0.0398990i	−0.183596	+	0.983002i	$0.558774\pi$
$464$		0			0
$465$	−0.569160	+	1.19422i	−0.0263942	+	0.0553804i
$466$		0			0
$467$	6.52807	+	6.52807i	0.302083	+	0.302083i	0.841828	−	0.539745i	$-0.181479\pi$
$467$	6.52807	+	6.52807i	0.302083	+	0.302083i	−0.539745	+	0.841828i	$0.681479\pi$
$468$		0			0
$469$	0.453066	+	0.261578i	0.0209206	+	0.0120785i
$470$		0			0
$471$	−2.24244	−	28.3812i	−0.103326	−	1.30774i
$472$		0			0
$473$	−6.88723	+	6.88723i	−0.316675	+	0.316675i
$474$		0			0
$475$	−13.6429	−	13.6429i	−0.625981	−	0.625981i
$476$		0			0
$477$	17.8661	−	14.4859i	0.818031	−	0.663263i
$478$		0			0
$479$	15.0944	−	4.04453i	0.689680	−	0.184799i	0.103077	−	0.994673i	$-0.467131\pi$
$479$	15.0944	−	4.04453i	0.689680	−	0.184799i	0.586604	+	0.809874i	$0.300465\pi$
$480$		0			0
$481$	−4.02100	−	12.4366i	−0.183342	−	0.567060i
$482$		0			0
$483$	0.831035	+	2.34447i	0.0378134	+	0.106677i
$484$		0			0
$485$	4.41624	+	7.64915i	0.200531	+	0.347330i
$486$		0			0
$487$	8.22774	−	8.22774i	0.372834	−	0.372834i	−0.495674	−	0.868509i	$-0.665079\pi$
$487$	8.22774	−	8.22774i	0.372834	−	0.372834i	0.868509	+	0.495674i	$0.165079\pi$
$488$		0			0
$489$	−10.6169	+	12.4385i	−0.480112	+	0.562490i
$490$		0			0
$491$			14.8640i			0.670802i	0.942076	+	0.335401i	$0.108872\pi$
$491$			14.8640i			0.670802i	−0.942076	+	0.335401i	$0.891128\pi$
$492$		0			0
$493$	−8.09461	+	14.0203i	−0.364563	+	0.631441i
$494$		0			0
$495$	2.79728	+	2.02971i	0.125729	+	0.0912289i
$496$		0			0
$497$	0.848309	+	0.489771i	0.0380519	+	0.0219693i
$498$		0			0
$499$	6.32351	−	23.5997i	0.283079	−	1.05647i	−0.667152	−	0.744921i	$-0.732487\pi$
$499$	6.32351	−	23.5997i	0.283079	−	1.05647i	0.950232	−	0.311545i	$-0.100846\pi$
$500$		0			0
$501$	12.7826	+	36.0618i	0.571087	+	1.61112i
$502$		0			0
$503$	−37.5229	+	10.0542i	−1.67307	+	0.448297i	−0.965935	−	0.258786i	$-0.916677\pi$
$503$	−37.5229	+	10.0542i	−1.67307	+	0.448297i	−0.707131	+	0.707083i	$0.750011\pi$
$504$		0			0
$505$	−2.26431	+	8.45054i	−0.100761	+	0.376044i
$506$		0			0
$507$	14.4743	−	1.14364i	0.642826	−	0.0507907i
$508$		0			0
$509$	−7.49010	+	12.9732i	−0.331993	+	0.575029i	−0.982903	−	0.184127i	$-0.941054\pi$
$509$	−7.49010	+	12.9732i	−0.331993	+	0.575029i	0.650910	+	0.759155i	$0.274388\pi$
$510$		0			0
$511$	0.140192	−	0.0809396i	0.00620171	−	0.00358056i
$512$		0			0
$513$	0.584867	−	23.1528i	0.0258225	−	1.02222i
$514$		0			0
$515$	2.75776	−	1.59219i	0.121522	−	0.0701605i
$516$		0			0
$517$			15.3702i			0.675981i
$518$		0			0
$519$	0.314238	+	3.97711i	0.0137935	+	0.174576i
$520$		0			0
$521$	2.27386	+	3.93844i	0.0996197	+	0.172546i	0.911527	−	0.411240i	$-0.134904\pi$
$521$	2.27386	+	3.93844i	0.0996197	+	0.172546i	−0.811908	+	0.583786i	$0.801571\pi$
$522$		0			0
$523$	14.4021	+	3.85902i	0.629759	+	0.168743i	0.559560	−	0.828790i	$-0.310970\pi$
$523$	14.4021	+	3.85902i	0.629759	+	0.168743i	0.0701985	+	0.997533i	$0.477637\pi$
$524$		0			0
$525$	1.26783	+	1.84349i	0.0553327	+	0.0804564i
$526$		0			0
$527$	−3.37090	−	1.94619i	−0.146839	−	0.0847773i
$528$		0			0
$529$			0.160103i			0.00696099i
$530$		0			0
$531$	−0.494975	+	4.73745i	−0.0214801	+	0.205588i
$532$		0			0
$533$	6.57132	+	24.5245i	0.284635	+	1.06227i
$534$		0			0
$535$	1.31549	+	4.90947i	0.0568735	+	0.212255i
$536$		0			0
$537$	2.24044	−	12.1092i	0.0966823	−	0.522549i
$538$		0			0
$539$	4.85881	−	8.41570i	0.209284	−	0.362490i
$540$		0			0
$541$	−13.1303	+	13.1303i	−0.564516	+	0.564516i	−0.930587	−	0.366071i	$-0.880703\pi$
$541$	−13.1303	+	13.1303i	−0.564516	+	0.564516i	0.366071	+	0.930587i	$0.380703\pi$
$542$		0			0
$543$	−3.63749	−	1.73362i	−0.156100	−	0.0743968i
$544$		0			0
$545$	−10.9741			−0.470079
$546$		0			0
$547$	16.2813	+	16.2813i	0.696137	+	0.696137i	0.963575	−	0.267438i	$-0.0861771\pi$
$547$	16.2813	+	16.2813i	0.696137	+	0.696137i	−0.267438	+	0.963575i	$0.586177\pi$
$548$		0			0
$549$	7.28960	+	5.28934i	0.311112	+	0.225744i
$550$		0			0
$551$	14.9669	−	8.64112i	0.637610	−	0.368124i
$552$		0			0
$553$	−0.373226	−	1.39290i	−0.0158712	−	0.0592321i
$554$		0			0
$555$	−5.26253	+	6.84210i	−0.223382	+	0.290431i
$556$		0			0
$557$	−3.62511	−	13.5291i	−0.153601	−	0.573247i	−0.999221	−	0.0394614i	$-0.987436\pi$
$557$	−3.62511	−	13.5291i	−0.153601	−	0.573247i	0.845620	−	0.533785i	$-0.179231\pi$
$558$		0			0
$559$	−12.8902	+	7.44214i	−0.545196	+	0.314769i
$560$		0			0
$561$	−6.60171	+	7.73443i	−0.278724	+	0.326548i
$562$		0			0
$563$	20.4328	+	20.4328i	0.861139	+	0.861139i	0.991471	−	0.130331i	$-0.0416041\pi$
$563$	20.4328	+	20.4328i	0.861139	+	0.861139i	−0.130331	+	0.991471i	$0.541604\pi$
$564$		0			0
$565$	4.79645			0.201788
$566$		0			0
$567$	−0.555152	+	2.62770i	−0.0233142	+	0.110353i
$568$		0			0
$569$	8.73461	−	8.73461i	0.366174	−	0.366174i	−0.499906	−	0.866080i	$-0.666632\pi$
$569$	8.73461	−	8.73461i	0.366174	−	0.366174i	0.866080	+	0.499906i	$0.166632\pi$
$570$		0			0
$571$	19.8386	−	34.3615i	0.830220	−	1.43798i	−0.0676438	−	0.997710i	$-0.521548\pi$
$571$	19.8386	−	34.3615i	0.830220	−	1.43798i	0.897864	−	0.440274i	$-0.145119\pi$
$572$		0			0
$573$	−1.01844	−	0.188432i	−0.0425458	−	0.00787185i
$574$		0			0
$575$	5.39174	+	20.1223i	0.224851	+	0.839156i
$576$		0			0
$577$	−5.97998	−	22.3176i	−0.248950	−	0.929093i	−0.971357	−	0.237625i	$-0.923631\pi$
$577$	−5.97998	−	22.3176i	−0.248950	−	0.929093i	0.722407	−	0.691468i	$-0.243036\pi$
$578$		0			0
$579$	−2.22404	+	12.0205i	−0.0924279	+	0.499555i
$580$		0			0
$581$		−	2.61650i		−	0.108551i
$582$		0			0
$583$	9.33629	+	5.39031i	0.386670	+	0.223244i
$584$		0			0
$585$	3.32625	+	4.10241i	0.137524	+	0.169614i
$586$		0			0
$587$	−42.6232	−	11.4209i	−1.75925	−	0.471389i	−0.772688	−	0.634786i	$-0.781088\pi$
$587$	−42.6232	−	11.4209i	−1.75925	−	0.471389i	−0.986560	+	0.163397i	$0.947755\pi$
$588$		0			0
$589$	2.07759	+	3.59849i	0.0856055	+	0.148273i
$590$		0			0
$591$	37.7314	−	2.98122i	1.55206	−	0.122631i
$592$		0			0
$593$			21.8316i			0.896517i	0.893904	+	0.448259i	$0.147956\pi$
$593$			21.8316i			0.896517i	−0.893904	+	0.448259i	$0.852044\pi$
$594$		0			0
$595$	0.884044	−	0.510403i	0.0362423	−	0.0209245i
$596$		0			0
$597$	2.10224	+	0.388958i	0.0860391	+	0.0159190i
$598$		0			0
$599$	10.8724	−	6.27716i	0.444232	−	0.256478i	−0.261159	−	0.965296i	$-0.584105\pi$
$599$	10.8724	−	6.27716i	0.444232	−	0.256478i	0.705391	+	0.708818i	$0.250771\pi$
$600$		0			0
$601$	−8.80478	+	15.2503i	−0.359155	+	0.622074i	−0.987820	−	0.155602i	$-0.950268\pi$
$601$	−8.80478	+	15.2503i	−0.359155	+	0.622074i	0.628665	+	0.777676i	$0.283602\pi$
$602$		0			0
$603$	0.825952	+	5.19414i	0.0336354	+	0.211522i
$604$		0			0
$605$	1.91329	−	7.14049i	0.0777863	−	0.290302i
$606$		0			0
$607$	−38.0509	+	10.1957i	−1.54444	+	0.413831i	−0.927696	−	0.373336i	$-0.878214\pi$
$607$	−38.0509	+	10.1957i	−1.54444	+	0.413831i	−0.616741	+	0.787166i	$0.711547\pi$
$608$		0			0
$609$	−1.88893	+	0.669558i	−0.0765431	+	0.0271319i
$610$		0			0
$611$	−6.07917	+	22.6878i	−0.245937	+	0.917850i
$612$		0			0
$613$	−11.4577	−	6.61513i	−0.462774	−	0.267183i	0.250436	−	0.968133i	$-0.419426\pi$
$613$	−11.4577	−	6.61513i	−0.462774	−	0.267183i	−0.713210	+	0.700951i	$0.752759\pi$
$614$		0			0
$615$	10.8857	−	12.7535i	0.438953	−	0.514269i
$616$		0			0
$617$	14.4682	−	25.0597i	0.582468	−	1.00886i	−0.412717	−	0.910859i	$-0.635420\pi$
$617$	14.4682	−	25.0597i	0.582468	−	1.00886i	0.995186	−	0.0980057i	$-0.0312463\pi$
$618$		0			0
$619$		−	23.9466i		−	0.962496i	−0.876585	−	0.481248i	$-0.840184\pi$
$619$		−	23.9466i		−	0.962496i	0.876585	−	0.481248i	$-0.159816\pi$
$620$		0			0
$621$	−13.0461	+	21.3336i	−0.523523	+	0.856087i
$622$		0			0
$623$	1.43438	−	1.43438i	0.0574671	−	0.0574671i
$624$		0			0
$625$	7.69092	+	13.3211i	0.307637	+	0.532843i
$626$		0			0
$627$	10.2316	−	3.62674i	0.408609	−	0.144838i
$628$		0			0
$629$	−18.8492	−	17.0214i	−0.751568	−	0.678687i
$630$		0			0
$631$	−19.0966	+	5.11693i	−0.760225	+	0.203702i	−0.618049	−	0.786140i	$-0.712077\pi$
$631$	−19.0966	+	5.11693i	−0.760225	+	0.203702i	−0.142176	+	0.989841i	$0.545410\pi$
$632$		0			0
$633$	−5.95738	+	4.09710i	−0.236785	+	0.162845i
$634$		0			0
$635$	1.99522	+	1.99522i	0.0791779	+	0.0791779i
$636$		0			0
$637$	10.5006	−	10.5006i	0.416048	−	0.416048i
$638$		0			0
$639$	1.54649	+	9.72538i	0.0611783	+	0.384730i
$640$		0			0
$641$	−6.17813	−	3.56695i	−0.244022	−	0.140886i	0.373002	−	0.927830i	$-0.378328\pi$
$641$	−6.17813	−	3.56695i	−0.244022	−	0.140886i	−0.617024	+	0.786945i	$0.711662\pi$
$642$		0			0
$643$	16.5674	+	16.5674i	0.653354	+	0.653354i	0.953799	−	0.300445i	$-0.0971352\pi$
$643$	16.5674	+	16.5674i	0.653354	+	0.653354i	−0.300445	+	0.953799i	$0.597135\pi$
$644$		0			0
$645$	8.87344	+	4.22906i	0.349391	+	0.166519i
$646$		0			0
$647$	−13.6620	−	3.66072i	−0.537108	−	0.143918i	−0.0199395	−	0.999801i	$-0.506347\pi$
$647$	−13.6620	−	3.66072i	−0.537108	−	0.143918i	−0.517169	+	0.855883i	$0.673014\pi$
$648$		0			0
$649$	−2.15649	+	0.577829i	−0.0846495	+	0.0226818i
$650$		0			0
$651$	−0.160982	−	0.454155i	−0.00630938	−	0.0177997i
$652$		0			0
$653$	−26.2947	−	7.04565i	−1.02899	−	0.275717i	−0.295447	−	0.955359i	$-0.595469\pi$
$653$	−26.2947	−	7.04565i	−1.02899	−	0.275717i	−0.733544	+	0.679642i	$0.762135\pi$
$654$		0			0
$655$	0.332764			0.0130022
$656$		0			0
$657$	1.51968	+	0.582275i	0.0592883	+	0.0227167i
$658$		0			0
$659$	−24.4337	−	42.3204i	−0.951802	−	1.64857i	−0.741523	−	0.670927i	$-0.765896\pi$
$659$	−24.4337	−	42.3204i	−0.951802	−	1.64857i	−0.210278	−	0.977642i	$-0.567437\pi$
$660$		0			0
$661$	7.04581	−	26.2953i	0.274050	−	1.02277i	−0.682425	−	0.730956i	$-0.739075\pi$
$661$	7.04581	−	26.2953i	0.274050	−	1.02277i	0.956475	−	0.291814i	$-0.0942587\pi$
$662$		0			0
$663$	−12.8038	+	8.80561i	−0.497258	+	0.341982i
$664$		0			0
$665$	−1.08973			−0.0422578
$666$		0			0
$667$	−18.6599			−0.722515
$668$		0			0
$669$	−11.8550	+	8.15309i	−0.458340	+	0.315217i
$670$		0			0
$671$	−1.09257	+	4.07752i	−0.0421781	+	0.157411i
$672$		0			0
$673$	−19.3772	−	33.5623i	−0.746936	−	1.29373i	−0.949285	−	0.314418i	$-0.898191\pi$
$673$	−19.3772	−	33.5623i	−0.746936	−	1.29373i	0.202349	−	0.979314i	$-0.435143\pi$
$674$		0			0
$675$	−6.36838	+	21.5725i	−0.245119	+	0.830325i
$676$		0			0
$677$	20.2088			0.776688			0.388344	−	0.921515i	$-0.373047\pi$
$677$	20.2088			0.776688			0.388344	+	0.921515i	$0.373047\pi$
$678$		0			0
$679$	−3.10742	−	0.832631i	−0.119252	−	0.0319534i
$680$		0			0
$681$	13.0187	+	36.7277i	0.498878	+	1.40741i
$682$		0			0
$683$	−21.4254	+	5.74093i	−0.819821	+	0.219670i	−0.644268	−	0.764799i	$-0.722838\pi$
$683$	−21.4254	+	5.74093i	−0.819821	+	0.219670i	−0.175553	+	0.984470i	$0.556171\pi$
$684$		0			0
$685$	10.9551	+	2.93542i	0.418574	+	0.112157i
$686$		0			0
$687$	−14.8315	−	7.06864i	−0.565856	−	0.269686i
$688$		0			0
$689$	11.6492	+	11.6492i	0.443800	+	0.443800i
$690$		0			0
$691$	−9.14650	−	5.28074i	−0.347949	−	0.200889i	0.315832	−	0.948815i	$-0.397716\pi$
$691$	−9.14650	−	5.28074i	−0.347949	−	0.200889i	−0.663782	+	0.747926i	$0.731050\pi$
$692$		0			0
$693$	−1.24319	+	0.197686i	−0.0472247	+	0.00750949i
$694$		0			0
$695$	2.69138	−	2.69138i	0.102090	−	0.102090i
$696$		0			0
$697$	34.8849	+	34.8849i	1.32136	+	1.32136i
$698$		0			0
$699$	24.1038	−	16.5770i	0.911689	−	0.627000i
$700$		0			0
$701$	−31.0480	+	8.31929i	−1.17267	+	0.314215i	−0.792014	−	0.610503i	$-0.790968\pi$
$701$	−31.0480	+	8.31929i	−1.17267	+	0.314215i	−0.380653	+	0.924718i	$0.624301\pi$
$702$		0			0
$703$	8.34074	+	25.7971i	0.314577	+	0.972957i
$704$		0			0
$705$	14.6204	−	5.18243i	0.550636	−	0.195181i
$706$		0			0
$707$	−1.59325	−	2.75959i	−0.0599204	−	0.103785i
$708$		0			0
$709$	18.6822	−	18.6822i	0.701626	−	0.701626i	−0.263133	−	0.964760i	$-0.584756\pi$
$709$	18.6822	−	18.6822i	0.701626	−	0.701626i	0.964760	+	0.263133i	$0.0847558\pi$
$710$		0			0
$711$	8.51397	−	11.7337i	0.319299	−	0.440047i
$712$		0			0
$713$		−	4.48641i		−	0.168017i
$714$		0			0
$715$	−1.23772	+	2.14380i	−0.0462883	+	0.0801736i
$716$		0			0
$717$	11.6786	−	13.6824i	0.436145	−	0.510978i
$718$		0			0
$719$	−6.20481	−	3.58235i	−0.231400	−	0.133599i	0.379818	−	0.925061i	$-0.375987\pi$
$719$	−6.20481	−	3.58235i	−0.231400	−	0.133599i	−0.611218	+	0.791462i	$0.709320\pi$
$720$		0			0
$721$	−0.300190	+	1.12032i	−0.0111797	+	0.0417231i
$722$		0			0
$723$	−1.41107	+	0.500177i	−0.0524784	+	0.0186018i
$724$		0			0
$725$	−16.2124	+	4.34409i	−0.602112	+	0.161335i
$726$		0			0
$727$	−3.31953	+	12.3887i	−0.123115	+	0.459470i	−0.999765	−	0.0216571i	$-0.993106\pi$
$727$	−3.31953	+	12.3887i	−0.123115	+	0.459470i	0.876651	+	0.481127i	$0.159772\pi$
$728$		0			0
$729$	−24.0345	+	12.3022i	−0.890166	+	0.455637i
$730$		0			0
$731$	−14.4608	+	25.0469i	−0.534854	+	0.926394i
$732$		0			0
$733$	5.32634	−	3.07517i	0.196733	−	0.113584i	−0.398398	−	0.917213i	$-0.630434\pi$
$733$	5.32634	−	3.07517i	0.196733	−	0.113584i	0.595131	+	0.803629i	$0.297100\pi$
$734$		0			0
$735$	−9.64342	−	1.78423i	−0.355703	−	0.0658123i
$736$		0			0
$737$	−2.13485	+	1.23256i	−0.0786383	+	0.0454018i
$738$		0			0
$739$			21.5878i			0.794122i	0.917792	+	0.397061i	$0.129970\pi$
$739$			21.5878i			0.794122i	−0.917792	+	0.397061i	$0.870030\pi$
$740$		0			0
$741$	16.5371	−	1.30663i	0.607507	−	0.0480001i
$742$		0			0
$743$	−0.811485	−	1.40553i	−0.0297705	−	0.0515640i	0.850756	−	0.525560i	$-0.176144\pi$
$743$	−0.811485	−	1.40553i	−0.0297705	−	0.0515640i	−0.880527	+	0.473996i	$0.842811\pi$
$744$		0			0
$745$	4.33663	+	1.16200i	0.158882	+	0.0425722i
$746$		0			0
$747$	20.4321	−	16.5664i	0.747570	−	0.606133i
$748$		0			0
$749$	−1.60323	−	0.925624i	−0.0585807	−	0.0338216i
$750$		0			0
$751$			32.7253i			1.19416i	0.802180	+	0.597082i	$0.203673\pi$
$751$			32.7253i			1.19416i	−0.802180	+	0.597082i	$0.796327\pi$
$752$		0			0
$753$	5.71842	−	30.9070i	0.208391	−	1.12631i
$754$		0			0
$755$	2.91155	+	10.8660i	0.105962	+	0.395456i
$756$		0			0
$757$	−10.9136	−	40.7301i	−0.396662	−	1.48036i	−0.818932	−	0.573891i	$-0.805433\pi$
$757$	−10.9136	−	40.7301i	−0.396662	−	1.48036i	0.422270	−	0.906470i	$-0.361233\pi$
$758$		0			0
$759$	−11.5251	−	2.13237i	−0.418334	−	0.0774003i
$760$		0			0
$761$	21.3210	−	36.9291i	0.772887	−	1.33868i	−0.163088	−	0.986612i	$-0.552145\pi$
$761$	21.3210	−	36.9291i	0.772887	−	1.33868i	0.935975	−	0.352068i	$-0.114521\pi$
$762$		0			0
$763$	2.82636	−	2.82636i	0.102321	−	0.102321i
$764$		0			0
$765$	9.58304	+	3.67181i	0.346476	+	0.132755i
$766$		0			0
$767$	−3.41170			−0.123190
$768$		0			0
$769$	−21.7401	−	21.7401i	−0.783970	−	0.783970i	0.196529	−	0.980498i	$-0.437033\pi$
$769$	−21.7401	−	21.7401i	−0.783970	−	0.783970i	−0.980498	+	0.196529i	$0.937033\pi$
$770$		0			0
$771$	−22.2370	+	26.0524i	−0.800846	+	0.938255i
$772$		0			0
$773$	24.2155	−	13.9808i	0.870972	−	0.502856i	0.00330113	−	0.999995i	$-0.498949\pi$
$773$	24.2155	−	13.9808i	0.870972	−	0.502856i	0.867671	+	0.497138i	$0.165616\pi$
$774$		0			0
$775$	−1.04445	−	3.89794i	−0.0375177	−	0.140018i
$776$		0			0
$777$	−0.406817	−	3.11753i	−0.0145945	−	0.111841i
$778$		0			0
$779$	−13.6308	−	50.8710i	−0.488376	−	1.82264i
$780$		0			0
$781$	−3.99724	+	2.30781i	−0.143033	+	0.0825799i
$782$		0			0
$783$	−17.1883	−	10.5112i	−0.614260	−	0.375638i
$784$		0			0
$785$	−9.52243	−	9.52243i	−0.339870	−	0.339870i
$786$		0			0
$787$	−49.1038			−1.75036			−0.875180	−	0.483797i	$-0.839257\pi$
$787$	−49.1038			−1.75036			−0.875180	+	0.483797i	$0.839257\pi$
$788$		0			0
$789$	−12.8277	−	6.11365i	−0.456678	−	0.217652i
$790$		0			0
$791$	−1.23532	+	1.23532i	−0.0439229	+	0.0439229i
$792$		0			0
$793$	−3.22545	+	5.58665i	−0.114539	+	0.198388i
$794$		0			0
$795$	1.97941	−	10.6983i	0.0702023	−	0.379430i
$796$		0			0
$797$	2.53843	+	9.47356i	0.0899159	+	0.335571i	0.996200	−	0.0870990i	$-0.0277597\pi$
$797$	2.53843	+	9.47356i	0.0899159	+	0.335571i	−0.906284	+	0.422670i	$0.861093\pi$
$798$		0			0
$799$	11.8125	+	44.0847i	0.417895	+	1.55960i
$800$		0			0
$801$	20.2827	+	2.11917i	0.716655	+	0.0748771i
$802$		0			0
$803$			0.762777i			0.0269178i
$804$		0			0
$805$	1.01896	+	0.588298i	0.0359137	+	0.0207348i
$806$		0			0
$807$	−25.1123	−	36.5145i	−0.883994	−	1.28537i
$808$		0			0
$809$	−47.0890	−	12.6175i	−1.65556	−	0.443607i	−0.694400	−	0.719589i	$-0.744330\pi$
$809$	−47.0890	−	12.6175i	−1.65556	−	0.443607i	−0.961163	+	0.275983i	$0.910997\pi$
$810$		0			0
$811$	−11.9267	−	20.6576i	−0.418803	−	0.725387i	0.577017	−	0.816732i	$-0.304217\pi$
$811$	−11.9267	−	20.6576i	−0.418803	−	0.725387i	−0.995819	+	0.0913450i	$0.970883\pi$
$812$		0			0
$813$	−0.445507	−	5.63850i	−0.0156246	−	0.197751i
$814$		0			0
$815$			7.73553i			0.270964i
$816$		0			0
$817$	26.7380	−	15.4372i	0.935444	−	0.540079i
$818$		0			0
$819$	−1.91324	−	0.199898i	−0.0668540	−	0.00698500i
$820$		0			0
$821$	−9.44861	+	5.45516i	−0.329759	+	0.190386i	−0.655734	−	0.754992i	$-0.727641\pi$
$821$	−9.44861	+	5.45516i	−0.329759	+	0.190386i	0.325975	+	0.945378i	$0.394307\pi$
$822$		0			0
$823$	19.5227	−	33.8144i	0.680520	−	1.17869i	−0.294303	−	0.955712i	$-0.595087\pi$
$823$	19.5227	−	33.8144i	0.680520	−	1.17869i	0.974822	−	0.222983i	$-0.0715793\pi$
$824$		0			0
$825$	−10.5098	+	0.830395i	−0.365904	+	0.0289107i
$826$		0			0
$827$	13.4961	−	50.3680i	0.469304	−	1.75147i	−0.172908	−	0.984938i	$-0.555316\pi$
$827$	13.4961	−	50.3680i	0.469304	−	1.75147i	0.642212	−	0.766527i	$-0.278017\pi$
$828$		0			0
$829$	35.3785	−	9.47963i	1.22874	−	0.329241i	0.414654	−	0.909979i	$-0.363903\pi$
$829$	35.3785	−	9.47963i	1.22874	−	0.329241i	0.814091	+	0.580738i	$0.197236\pi$
$830$		0			0
$831$	−3.39791	−	9.58601i	−0.117872	−	0.332535i
$832$		0			0
$833$	7.46827	−	27.8720i	0.258760	−	0.965707i
$834$		0			0
$835$	15.6733	+	9.04897i	0.542396	+	0.313152i
$836$		0			0
$837$	2.52720	−	4.13259i	0.0873529	−	0.142843i
$838$		0			0
$839$	18.0726	−	31.3027i	0.623936	−	1.08069i	−0.364809	−	0.931082i	$-0.618866\pi$
$839$	18.0726	−	31.3027i	0.623936	−	1.08069i	0.988745	−	0.149607i	$-0.0478010\pi$
$840$		0			0
$841$			13.9658i			0.481581i
$842$		0			0
$843$	3.94902	−	4.62659i	0.136012	−	0.159348i
$844$		0			0
$845$	4.85640	−	4.85640i	0.167065	−	0.167065i
$846$		0			0
$847$	1.34626	+	2.33179i	0.0462580	+	0.0801212i
$848$		0			0
$849$	14.0773	+	39.7142i	0.483132	+	1.36299i
$850$		0			0
$851$	6.12769	−	28.6247i	0.210055	−	0.981243i
$852$		0			0
$853$	18.7517	−	5.02449i	0.642044	−	0.172035i	0.0769151	−	0.997038i	$-0.475493\pi$
$853$	18.7517	−	5.02449i	0.642044	−	0.172035i	0.565129	+	0.825002i	$0.308826\pi$
$854$		0			0
$855$	−6.89963	−	8.50960i	−0.235962	−	0.291022i
$856$		0			0
$857$	3.80945	+	3.80945i	0.130128	+	0.130128i	0.769171	−	0.639043i	$-0.220669\pi$
$857$	3.80945	+	3.80945i	0.130128	+	0.130128i	−0.639043	+	0.769171i	$0.720669\pi$
$858$		0			0
$859$	14.3197	−	14.3197i	0.488582	−	0.488582i	−0.419276	−	0.907859i	$-0.637716\pi$
$859$	14.3197	−	14.3197i	0.488582	−	0.488582i	0.907859	+	0.419276i	$0.137716\pi$
$860$		0			0
$861$	0.481041	+	6.08822i	0.0163938	+	0.207486i
$862$		0			0
$863$	−36.7084	−	21.1936i	−1.24957	−	0.721438i	−0.278544	−	0.960423i	$-0.589852\pi$
$863$	−36.7084	−	21.1936i	−1.24957	−	0.721438i	−0.971023	+	0.238985i	$0.923185\pi$
$864$		0			0
$865$	1.33440	+	1.33440i	0.0453709	+	0.0453709i
$866$		0			0
$867$	−0.322669	+	0.677026i	−0.0109584	+	0.0229930i
$868$		0			0
$869$	6.56336	+	1.75865i	0.222647	+	0.0596580i
$870$		0			0
$871$	−3.63873	+	0.974994i	−0.123294	+	0.0330364i
$872$		0			0
$873$	−13.1727	−	29.5375i	−0.445829	−	0.999691i
$874$		0			0
$875$	2.20305	+	0.590306i	0.0744767	+	0.0199560i
$876$		0			0
$877$	37.4443			1.26441			0.632203	−	0.774803i	$-0.282151\pi$
$877$	37.4443			1.26441			0.632203	+	0.774803i	$0.282151\pi$
$878$		0			0
$879$	6.76894	−	14.2026i	0.228311	−	0.479043i
$880$		0			0
$881$	−21.9509	−	38.0200i	−0.739543	−	1.28093i	−0.952701	−	0.303909i	$-0.901708\pi$
$881$	−21.9509	−	38.0200i	−0.739543	−	1.28093i	0.213158	−	0.977018i	$-0.431625\pi$
$882$		0			0
$883$	−10.2424	+	38.2251i	−0.344684	+	1.28638i	0.548297	+	0.836284i	$0.315276\pi$
$883$	−10.2424	+	38.2251i	−0.344684	+	1.28638i	−0.892981	+	0.450094i	$0.851390\pi$
$884$		0			0
$885$	1.27675	+	1.85646i	0.0429175	+	0.0624042i
$886$		0			0
$887$	44.5643			1.49632			0.748161	−	0.663517i	$-0.230937\pi$
$887$	44.5643			1.49632			0.748161	+	0.663517i	$0.230937\pi$
$888$		0			0
$889$	−1.02773			−0.0344690
$890$		0			0
$891$	−9.41497	−	8.45630i	−0.315413	−	0.283297i
$892$		0			0
$893$	12.6100	−	47.0611i	0.421977	−	1.57484i
$894$		0			0
$895$	−2.91256	−	5.04470i	−0.0973560	−	0.168626i
$896$		0			0
$897$	−16.1686	−	7.70593i	−0.539855	−	0.257293i
$898$		0			0
$899$	3.61467			0.120556
$900$		0			0
$901$	30.9209	+	8.28522i	1.03012	+	0.276021i
$902$		0			0
$903$	−3.37453	+	1.19615i	−0.112297	+	0.0398055i
$904$		0			0
$905$	−1.84109	+	0.493319i	−0.0611999	+	0.0163985i
$906$		0			0
$907$	−42.7218	−	11.4473i	−1.41855	−	0.380100i	−0.533584	−	0.845747i	$-0.679155\pi$
$907$	−42.7218	−	11.4473i	−1.41855	−	0.380100i	−0.884971	+	0.465647i	$0.845822\pi$
$908$		0			0
$909$	11.4618	−	29.9140i	0.380163	−	0.992185i
$910$		0			0
$911$	4.93313	+	4.93313i	0.163442	+	0.163442i	0.784090	−	0.620648i	$-0.213130\pi$
$911$	4.93313	+	4.93313i	0.163442	+	0.163442i	−0.620648	+	0.784090i	$0.713130\pi$
$912$		0			0
$913$	10.6772	+	6.16449i	0.353364	+	0.204015i
$914$		0			0
$915$	4.24699	−	0.335562i	0.140401	−	0.0110933i
$916$		0			0
$917$	−0.0857029	+	0.0857029i	−0.00283016	+	0.00283016i
$918$		0			0
$919$	−22.8842	−	22.8842i	−0.754881	−	0.754881i	0.220505	−	0.975386i	$-0.429229\pi$
$919$	−22.8842	−	22.8842i	−0.754881	−	0.754881i	−0.975386	+	0.220505i	$0.929229\pi$
$920$		0			0
$921$	26.2765	+	38.2074i	0.865841	+	1.25898i
$922$		0			0
$923$	−6.81306	+	1.82555i	−0.224255	+	0.0600888i
$924$		0			0
$925$	−1.33999	−	26.2966i	−0.0440585	−	0.864628i
$926$		0			0
$927$	−10.6492	+	4.74919i	−0.349765	+	0.155984i
$928$		0			0
$929$	3.39347	+	5.87766i	0.111336	+	0.192840i	0.916309	−	0.400472i	$-0.131154\pi$
$929$	3.39347	+	5.87766i	0.111336	+	0.192840i	−0.804973	+	0.593311i	$0.797820\pi$
$930$		0			0
$931$	−21.7813	+	21.7813i	−0.713853	+	0.713853i
$932$		0			0
$933$	−38.7209	−	33.0502i	−1.26767	−	1.08201i
$934$		0			0
$935$			4.81005i			0.157305i
$936$		0			0
$937$	21.5995	−	37.4115i	0.705626	−	1.22218i	−0.260839	−	0.965382i	$-0.583999\pi$
$937$	21.5995	−	37.4115i	0.705626	−	1.22218i	0.966465	−	0.256798i	$-0.0826676\pi$
$938$		0			0
$939$	10.0546	+	8.58204i	0.328118	+	0.280064i
$940$		0			0
$941$	35.3411	+	20.4042i	1.15209	+	0.665158i	0.949395	−	0.314085i	$-0.101698\pi$
$941$	35.3411	+	20.4042i	1.15209	+	0.665158i	0.202692	+	0.979242i	$0.435031\pi$
$942$		0			0
$943$	−14.7174	+	54.9262i	−0.479266	+	1.78864i
$944$		0			0
$945$	0.607212	+	1.11588i	0.0197526	+	0.0362997i
$946$		0			0
$947$	−22.8777	+	6.13006i	−0.743426	+	0.199200i	−0.610600	−	0.791939i	$-0.709072\pi$
$947$	−22.8777	+	6.13006i	−0.743426	+	0.199200i	−0.132826	+	0.991139i	$0.542405\pi$
$948$		0			0
$949$	−0.301691	+	1.12593i	−0.00979330	+	0.0365491i
$950$		0			0
$951$	4.32414	+	54.7279i	0.140220	+	1.77467i
$952$		0			0
$953$	−28.5262	+	49.4088i	−0.924054	+	1.60051i	−0.130979	+	0.991385i	$0.541812\pi$
$953$	−28.5262	+	49.4088i	−0.924054	+	1.60051i	−0.793075	+	0.609124i	$0.791521\pi$
$954$		0			0
$955$	−0.424282	+	0.244960i	−0.0137295	+	0.00792670i
$956$		0			0
$957$	1.71804	−	9.28566i	0.0555363	−	0.300163i
$958$		0			0
$959$	−3.57749	+	2.06546i	−0.115523	+	0.0666973i
$960$		0			0
$961$		−	30.1309i		−	0.971965i
$962$		0			0
$963$	−2.92273	−	18.3801i	−0.0941837	−	0.592291i
$964$		0			0
$965$	2.89123	+	5.00776i	0.0930720	+	0.161205i
$966$		0			0
$967$	−35.8321	−	9.60118i	−1.15228	−	0.308753i	−0.368403	−	0.929666i	$-0.620095\pi$
$967$	−35.8321	−	9.60118i	−1.15228	−	0.308753i	−0.783880	+	0.620913i	$0.786762\pi$
$968$		0			0
$969$	26.5588	−	18.2654i	0.853193	−	0.586770i
$970$		0			0
$971$	9.59093	+	5.53733i	0.307788	+	0.177701i	0.645936	−	0.763392i	$-0.276467\pi$
$971$	9.59093	+	5.53733i	0.307788	+	0.177701i	−0.338148	+	0.941093i	$0.609801\pi$
$972$		0			0
$973$			1.38632i			0.0444435i
$974$		0			0
$975$	−15.8418	−	2.93106i	−0.507344	−	0.0938689i
$976$		0			0
$977$	4.62017	+	17.2427i	0.147812	+	0.551643i	0.999614	+	0.0277788i	$0.00884339\pi$
$977$	4.62017	+	17.2427i	0.147812	+	0.551643i	−0.851802	+	0.523864i	$0.824490\pi$
$978$		0			0
$979$	2.47389	+	9.23269i	0.0790659	+	0.295078i
$980$		0			0
$981$	39.9660	+	4.17571i	1.27602	+	0.133320i
$982$		0			0
$983$	20.1423	−	34.8875i	0.642439	−	1.11274i	−0.342448	−	0.939537i	$-0.611256\pi$
$983$	20.1423	−	34.8875i	0.642439	−	1.11274i	0.984887	−	0.173200i	$-0.0554107\pi$
$984$		0			0
$985$	12.6596	−	12.6596i	0.403369	−	0.403369i
$986$		0			0
$987$	−2.43074	+	5.10019i	−0.0773712	+	0.162341i
$988$		0			0
$989$	−33.3356			−1.06001
$990$		0			0
$991$	−2.84174	−	2.84174i	−0.0902709	−	0.0902709i	0.660529	−	0.750800i	$-0.270332\pi$
$991$	−2.84174	−	2.84174i	−0.0902709	−	0.0902709i	−0.750800	+	0.660529i	$0.770332\pi$
$992$		0			0
$993$	13.5536	+	11.5686i	0.430109	+	0.367119i
$994$		0			0
$995$	0.875798	−	0.505642i	0.0277647	−	0.0160299i
$996$		0			0
$997$	−11.5050	−	42.9374i	−0.364368	−	1.35984i	−0.868276	−	0.496082i	$-0.834771\pi$
$997$	−11.5050	−	42.9374i	−0.364368	−	1.35984i	0.503908	−	0.863758i	$-0.331895\pi$
$998$		0			0
$999$	21.7688	−	22.9155i	0.688734	−	0.725014i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	888.2.br.a.569.8	yes	152
3.2	odd	2	inner	888.2.br.a.569.6	✓	152
37.8	odd	12	inner	888.2.br.a.785.6	yes	152
111.8	even	12	inner	888.2.br.a.785.8	yes	152

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
888.2.br.a.569.6	✓	152	3.2	odd	2	inner
888.2.br.a.569.8	yes	152	1.1	even	1	trivial
888.2.br.a.785.6	yes	152	37.8	odd	12	inner
888.2.br.a.785.8	yes	152	111.8	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 888 = 2^{3} \cdot 3 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	888.br (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.42713 + 0.981484i) q^{3} +(-0.212050 + 0.791381i) q^{5} +(-0.149206 - 0.258432i) q^{7} +(1.07338 - 2.80140i) q^{9} +1.40612 q^{11} +(2.07555 + 0.556143i) q^{13} +(-0.474106 - 1.33752i) q^{15} +(4.03302 - 1.08064i) q^{17} +(-4.30531 - 1.15360i) q^{19} +(0.466582 + 0.222372i) q^{21} +(3.40295 + 3.40295i) q^{23} +(3.74881 + 2.16438i) q^{25} +(1.21769 + 5.05146i) q^{27} +(-2.74173 + 2.74173i) q^{29} +(-0.659194 - 0.659194i) q^{31} +(-2.00671 + 1.38008i) q^{33} +(0.236157 - 0.0632781i) q^{35} +(-3.30552 - 5.10622i) q^{37} +(-3.50792 + 1.24344i) q^{39} +(5.90794 + 10.2328i) q^{41} +(-4.89804 + 4.89804i) q^{43} +(1.98937 + 1.44349i) q^{45} +10.9310i q^{47} +(3.45548 - 5.98506i) q^{49} +(-4.69499 + 5.50055i) q^{51} +(6.63976 + 3.83347i) q^{53} +(-0.298167 + 1.11277i) q^{55} +(7.27646 - 2.57925i) q^{57} +(-1.53365 + 0.410939i) q^{59} +(-0.777010 + 2.89984i) q^{61} +(-0.884126 + 0.140590i) q^{63} +(-0.880242 + 1.52462i) q^{65} +(-1.51826 + 0.876567i) q^{67} +(-8.19637 - 1.51650i) q^{69} +(-2.84275 + 1.64126i) q^{71} +0.542470i q^{73} +(-7.47432 + 0.590559i) q^{75} +(-0.209801 - 0.363386i) q^{77} +(4.66772 + 1.25071i) q^{79} +(-6.69572 - 6.01393i) q^{81} +(7.59339 + 4.38405i) q^{83} +3.42080i q^{85} +(1.22183 - 6.60376i) q^{87} +(1.75938 + 6.56608i) q^{89} +(-0.165959 - 0.619369i) q^{91} +(1.58774 + 0.293765i) q^{93} +(1.82588 - 3.16252i) q^{95} +(7.62300 - 7.62300i) q^{97} +(1.50930 - 3.93910i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 152 q + 4 q^{13} - 12 q^{15} + 4 q^{19} - 44 q^{31} - 12 q^{39} + 28 q^{43} + 20 q^{45} - 80 q^{49} - 12 q^{51} - 8 q^{55} - 40 q^{57} - 28 q^{61} + 48 q^{63} + 56 q^{69} + 64 q^{75} + 20 q^{79} + 16 q^{81}+ \cdots - 20 q^{97}+O(q^{100}) \) 152 * q + 4 * q^13 - 12 * q^15 + 4 * q^19 - 44 * q^31 - 12 * q^39 + 28 * q^43 + 20 * q^45 - 80 * q^49 - 12 * q^51 - 8 * q^55 - 40 * q^57 - 28 * q^61 + 48 * q^63 + 56 * q^69 + 64 * q^75 + 20 * q^79 + 16 * q^81 + 56 * q^87 + 52 * q^91 + 40 * q^93 - 20 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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